# Reverse engineering scratchie tickets

After reading an article about how one man “cracked” extended play scratch lottery cards, I decided to give it a go myself, armed only with \$18 and an abundance of free time. I bought six of SA lotto’s crossword type games and sat down to analyse them.

Normal “quick play” scratchie cards are impossible to beat. They give nothing away until you scratch them. “Extended play” cards are different. Here’s what the ones I bought look like:

At the top of the card are 20 letters hidden beneath the scratchable area. These are hidden until you buy the card. At the bottom of the card is a crossword. This part you can see before you buy it. To play the game you scratch off the letters at the top, and see how many words from the crossword you can “find” using those letters. 3 or more and you win.

Because you can see the crossword before you buy the ticket, it could potentially give away information about whether or not the card is a winner. It all depends on the method they use to generate the crossword and the hidden letters in the first place. All that’s needed is a little reverse engineering.

I had six cards to work from. Looking at each of the cards I found that they all had 10 “across” words and 11 “down” words (21 words in total). Each card also had the 20 letters to scratch off, the key to the puzzle. I spent some time with a pen and paper looking at things such as the frequency of each letter on the various cards, but i was getting nowhere – time to switch to the computer.

So if I was designing this scratchie ticket system, how would I go about it? The key to the puzzle is the 20 scratchable letters. Taking the 6 crosswords available to me, could I generate a new set of 20 different letters that would make them winners? Or losers? If I couldn’t then there might be a flaw in the system that could be exploited.

Here’s how that logic works; take a look at this card:

“Pinball”, “nomad” and “lap” are the only words we can make. You need three or more words to win, so here we have won \$4. If we can’t come up with some different combination of 20 letters that will make this card a loser, then that would make this card identifiable as a guaranteed winner – without having had to scratch off the numbers first. This is easy enough to do, we simply replace the “i” that makes up “pinball” with a “z” and we have a loser (of course all the “loser” cards I found had two words made, to make people think they had almost won).

Being me, I had to go into overkill mode and work out exactly how many different loser combinations there were for each card, so I wrote a program to do it. It turns out that there are 2395 different losing combinations for this card (meaning only two words made). This is bad news for us. It means that we can’t look at the just the crossword to find out whether a card is a loser, and therefore decide not to buy it.

But what about looking at things the other way around? The grand prize for finding ten words is \$100,000. If we can’t take a losing card and generate 20 letters that turn it into a grand prize winner, then we might be able to narrow the field down. We could identify which cards are definitely not grand prize winners, and only buy cards that have a real chance. Depending on the numbers, this might pay off. For example if only 1 in 1000 cards are identified as potential grand prize winners (before buying them), and 1 in 500,000 cards are actual grand prize winners, then we’d only need to buy 500 cards to win (on average). At \$3 a card that would cost \$1500, giving us a tidy profit of \$98,500.

So can we do it? If we can turn any old loser card into a grand prize winner just by picking different letters, then the answer is no. So that’s what I set out to do, using my bag of tricks. Here’s one of the cards I looked at.

It turns out the letters `abdefhiklopqstuvwxyz` could make this a grand prize winner (try it), along with 2886 other different combinations of letters. Sorry to disappoint folks but it looks like the system is sound, and this scratchie system isn’t easily crackable. Of course there still might be some flaw in the way they specifically generate the cards, but it looks at least possible to create an uncrackable system using this crossword-and-20-hidden-letter scheme, as it appears that each card can be easily switched from a winner to a loser or vice versa just by changing the hidden letters.

At least I had fun investigating it. And in case you are wondering, of the six cards that I bought, 2 were winners. Or so I thought. I took photos of them all for later analysis on the computer and threw the “losers” out. Later when I actually did the analysis, I found one more winner I had mistakenly thrown out. Let that be a lesson to you all – in gambling, even when you win, you lose.

# Lotto roulette

So Kath wrote about playing the lotto, and why she does it. I started to write a reply which turned out to be insanely long, so long that it deserves republishing here.

I’ve never understood why people seem to get a thrill from buying a lotto ticket and imagining what they will do if they win. See, the thing is, imagination is free. You don’t actually need to buy the ticket to indulge in the “what would I do if I won lotto” game.

You could imagine that you found a ticket. You could imagine that some mysterious distant relative you’ve never heard of has carked it and you’ve inherited their estate. You could imagine charlie and the chocolate factory is real, and you’ve just laid your hands on the golden ticket.

None of this costs you anything.

And obviously you know how improbable it is to win, but you convince yourself otherwise. So quoting numbers isn’t going to win you over, but maybe visualizing it will. So here goes…

Google tells me the odds of winning oz lotto are 8,145,060 to 1. Let’s imagine these odds on a roulette table.

Let’s assume our roulette ball is 1cm wide. So it needs to fall into a slot that is at least 1cm wide. And there needs to be 8,145,060 slots. So that makes a roulette wheel with a circumference of at least 81 km. The good ol’ 2 pi R formula tells us that would make the wheel about 26km across.

This is way bigger than the biggest circular thing I can think of, the Arecibo radio observatory. Take a look at this picture of it.

Imagine playing roulette on that baby, hoping your ball will fall into the 1cm wide slot on the edge with your number on it.

That radio telescope is only 305 metres wide. The imaginary “lotto” roulette wheel is 26km wide; 86 times bigger! It might take you an hour of driving around it just to see who won, if you were doing 80km/hr! Assuming you can even spot a 1cm wide roulette ball at that speed!

Wow it was fun working that out and imagining it. And it cost me nothing! In conclusion, I am a total nerd and you should not buy lotto tickets.